Heptagram

A heptagram, septagram, septegram or septogram is a seven-point star drawn with seven straight strokes.

"Elven star" redirects here. For the book by Margaret Weis and Tracy Hickman, see Elven Star.
Regular heptagram (7/2)
A regular heptagram
TypeRegular star polygon
Edges and vertices7
Schläfli symbol{7/2}
Coxeter diagram
Symmetry groupDihedral (D7)
Internal angle (degrees)≈77.143°
Dual polygonself
PropertiesStar, cyclic, equilateral, isogonal, isotoxal
Regular heptagram (7/3)
A regular heptagram
TypeRegular star polygon
Edges and vertices7
Schläfli symbol{7/3}
Coxeter diagram
Symmetry groupDihedral (D7)
Internal angle (degrees)≈25.714°
Dual polygonself
PropertiesStar, cyclic, equilateral, isogonal, isotoxal
Star polygons

The name heptagram combines a numeral prefix, hepta-, with the Greek suffix -gram. The -gram suffix derives from γραμμῆ (grammē) meaning a line.[1]

Geometry

In general, a heptagram is any self-intersecting heptagon (7-sided polygon).

There are two regular heptagrams, labeled as {7/2} and {7/3}, with the second number representing the vertex interval step from a regular heptagon, {7/1}.

This is the smallest star polygon that can be drawn in two forms, as irreducible fractions. The two heptagrams are sometimes called the heptagram (for {7/2}) and the great heptagram (for {7/3}).

The previous one, the regular hexagram {6/2}, is a compound of two triangles. The smallest star polygon is the {5/2} pentagram.

The next one is the {8/3} octagram and its related {8/2} star figure (a compound of two squares), followed by the regular enneagram, which also has two forms: {9/2} and {9/4}, as well as one compound of three triangles {9/3}.


{7/2}
{7/3}
{7}+{7/2}+{7/3}

7-2 prism
7-3 prism
Complete graph

7-2 antiprism
7-3 antiprism
7-4 antiprism


Uses

Flags and heraldry
  • Former Georgian coat of arms, 1918–1921, 1991–2004
  • Roundel of the Georgian Air Force
  • Flag of Eastern Band Cherokee
  • The seven-pointed star of the Felibritge on the Occitan flag.
  • The Jordanian flag, bearing the star that symbolizes Al-Fatiha
  • Symbol of Hokkaido
  • Coat of arms of Samarkand
  • Commonwealth Star as the crest of Coat of Arms of Australia

Law enforcement

Religious and occult symbolism
Seal of Babalon and the A∴A∴
  • The heptagram was used in Christianity to symbolize the seven days of creation and became a traditional symbol for warding off evil. The symbol is used in some Christian sects such as Catholicism and Orthodox Christianity.
  • The symbol is also used in Kabbalist Judaism.
  • In Islam, the heptagram is used to represent the first seven verses in the Quran.
  • The heptagram is used in the symbol for Babalon in Thelema.
  • The heptagram is known among neopagans as the Elven Star or Fairy Star. It is treated as a sacred symbol in various modern pagan and witchcraft traditions. Blue Star Wicca also uses the symbol, where it is referred to as a septegram. The second heptagram is a symbol of magical power in some pagan spiritualities.
  • In alchemy, a seven-sided star can refer to the seven planets which were known to early alchemists.
  • In Polynesia, the seven-pointed star is used often in imagery, basket making, tattoos, and is considered to be a symbol of Kanaloa, the first Polynesian navigator. [2]. [3]
Logo of Maersk
  • The logo of american shoe brand DC Shoes features a 7/3 heptagram in the letter C.
  • The seven-pointed star is used as the logo for the international Danish shipping company A.P. Moller–Maersk Group, sometimes known simply as Maersk.
  • In George R. R. Martin's novel series A Song of Ice and Fire and its TV version Game of Thrones, a seven-pointed star serves as the symbol of the Faith of the Seven.
  • Progressive metal band Tool uses the heptagram in their art and visuals as a symbol of positive energy and openness.
  • In the manga series MeruPuri, a magical mirror/ portal is in the shape of a heptagram. The symbol is also seen during spellcasting.
  • Finnish rock band HIM used a heptagram on the cover of their eighth studio album Tears on Tape.
  • American heavy metal band Darkest Hour used a heptagram on the cover of their eighth studio album Darkest Hour.
  • English Singer Damon Albarn uses a heptagram as a symbol in his solo performances.
  • The {7/3} heptagram is used by some members of the otherkin subculture as an identifier.
  • The American Progressive Rock Metal Band “Tool” uses an ‘open’ seven pointed symbol for their fan group, The Tool Army. It is ‘open’ to signify an invitation into the collective unconscious.
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See also

References
  1. γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
  2. https://www.huna.org
  3. https://www.amazon.com/Children-Rainbow-Religions-Legends-Pre-Christian/dp/0835600025

Bibliography

  • Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
  • Grünbaum, B.; Polyhedra with Hollow Faces, Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43–70.
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)
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